PI354X-00 Datasheet, PDF (31/39 Pages) –

PI354x-00
( )_/(( ) ( )) G_LED(s) = g_MOD • r_EQ • R_SHUNT
R_SHUNT + R_LED + r_EQ + s C_OUT • r_EQ • R_LED+ R_SHUNT • r_EQ • C_OUT
(12)
(( )_// ) ^{FP_LED =} 2 • π •
1
R_LED + R_SHUNT
r_EQ • C_OUT
= 1.2kHz
(13)
( ⁽ ) ⁾ ) ^{GLGH_EAO(s) = EINT (s) • ELS • GMLGH •}
R_OUT + s R_ZI • C_COMP • R_OUT
1 + s • C_COMP + C_HF + s² • (C_HF • C_COMP • R_ZI
(14)
Where:
( ) ^{EINT (s) = EINT •}
1+s•
1
R_LGH • C_INT • E_INT
(15)
( _// ) ^{FP_HF =}
2•π•
C_HF + C_COMP
R_ZI R_OUT • C_COMP • C_HF
= 580kHz
(16)
The integrator pole is determined by the external input resistor R_LGH and the internal C_INT, which is 20pF. Assuming R_LGH = 100kΩ and
E_INT = 2500:
80
60
40
20
0
20
40
1
0
Gain - dBV
Phase-Degrees
20
40
60
80
100
10
100
1000
10000
100000
Frequency- Hz
Figure 63 — E_INT(s) Gain/Phase Plot R_LGH = 100kΩ
80
60
40
20
0
1
0
Gain - dBV
Phase-Degrees
20
40
60
80
100
10
100
1000
10000
100000
1000000
Frequency- Hz
Figure 64 — GM_LGH(s) Gain/Phase Plot Voltage Loop Open
Cool-Power^® ZVS Switching Regulators
Page 31 of 39
Rev 1.6
03/2017
150
100
50
0
50
1
0
Gain - dBV
Phase-Degrees
50
100
150
10
100
1000
10000
100000
1000000
Frequency- Hz
Figure 65 — G_{LGH_EAO}(s) Gain/Phase Plot R_LGH = 100kΩ
When combining Figure 63 with Figure 64, it becomes clear
that additional compensation is needed to have enough phase
and gain margin like can be seen with the voltage loop plot. We
can remedy that easily, by adding a series R-C in parallel with
R_LGH as shown in the lighting application diagram in Figure 59.
The capacitor will be chosen to work with R_LGH to add a zero
approximately 1.2kHz before the zero provided by the GM_LGH(s)
transfer function (the trans-conductance stage of the LGH
amplifier). This value will be chosen to be 270pF. The external
added resistor will form a high frequency pole to roll the gain
off at higher frequency. This pole will be set at approximately
120kHz so a common 4.99kΩ resistor will be used. The resulting
Bode plot with the new compensator of G_{LGH_EAO}(s) can be seen
in Figure 66. Figure 67 shows the final Bode plot of the loop gain
when using a lighting application with LED’s operating in constant
current mode. Note that it is very important to understand the
AC resistance of the LEDs that are being used. Please consult the
LED manufacturer for details. For a series string, you should add
the individual LED resistances and combine them into one lumped
value to simplify the analysis.
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